Finite Group Databasebeta

← #7053272

Subgroups — #7053272

Order 512.

1542 conjugacy classes of subgroups.

The subgroup lattice has 1291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59820C211yesmaximal, characteristic, complemented
2#59257C211yesmaximal, characteristic, complemented
3#32666C211yesmaximal, characteristic, complemented
4#32623C211yesmaximal, characteristic, complemented
5#32401C211yesmaximal, characteristic, complemented
6#32308C211yesmaximal, characteristic, complemented
7#31958C211yesmaximal, characteristic, complemented
8#31597C211yesmaximal, characteristic, complemented
9#31314C211yesmaximal, characteristic, complemented
10#31000C211yesmaximal, characteristic
11#29408C211yesmaximal, characteristic, complemented
12#29028C211yesmaximal, characteristic, complemented
13#28038C211yesmaximal, characteristic, complemented
14#27585C211yesmaximal, characteristic, complemented
15#27571C211yesmaximal, characteristic, complemented
16#27534C211yesmaximal, characteristic, complemented
17#27495C211yesmaximal, characteristic, complemented
18#27470C211yesmaximal, characteristic, complemented
19#27365C211yesmaximal, characteristic, complemented
20#27199C211yesmaximal, characteristic, complemented
21#27174C211yesmaximal, characteristic, complemented
22#26755C211yesmaximal, characteristic, complemented
23#26334C211yesmaximal, characteristic, complemented
24#26174C211yesmaximal, characteristic, complemented
25#25007C211yesmaximal, characteristic, complemented
26#24909C211yesmaximal, characteristic, complemented
27#23755C211yesmaximal, characteristic, complemented
28#23108C211yesmaximal, characteristic, complemented
29#22817C211yesmaximal, characteristic, complemented
30#22325C211yesmaximal, characteristic, complemented
31#22040C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#459C2211yescharacteristic
34C2×#447C2211yescharacteristic
35C2×#442C2211yescharacteristic
36#2750—21no—
37#2750—21no—
38#2730—21no—
39#2705—21no—
40#2573—21no—
41#2573—21no—
42#2571C2211yescharacteristic, complemented
43#2548C2211yescharacteristic
44#2538C2211yescharacteristic
45#2538C2211yescharacteristic, complemented
46#2534—21no—
47#2512C2211yescharacteristic
48#2512C2211yescharacteristic
49#2509C2211yescharacteristic, complemented
50#2509C2211yescharacteristic, complemented
51#2503—21no—
52#2501C2211yescharacteristic
53#2495—21no—
54#2495C2211yescharacteristic
55#2495C2211yescharacteristic
56#2471—21no—
57#2467—21no—
58#2445C2211yescharacteristic
59#2445C2211yescharacteristic
60#2433C2211yescharacteristic
61#2420C2211yescharacteristic
62#2420C2211yescharacteristic
63#2415—21no—
64#2412—21no—
65#2411—21no—
66#2366C2211yescharacteristic
67#2357C2211yescharacteristic, complemented
68#2357C2211yescharacteristic, complemented
69#2355C2211yescharacteristic, complemented
70#2354C2211yescharacteristic
71#2352—21no—
72D4×C4⋊C4C2211yescharacteristic, complemented
73#2344C2211yescharacteristic
74D4×C22⋊C4C2211yescharacteristic
75C4×C22⋊Q8C2211yescharacteristic
76C4×#121C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#390C2211yescharacteristic
79#2285C2211yescharacteristic
80#2101C2211yescharacteristic, complemented
81#2100C2211yescharacteristic, complemented
82#2100C2211yescharacteristic, complemented
83#2094C2211yescharacteristic
84#2094C2211yescharacteristic
85#2094C2211yescharacteristic, complemented
86#2094C2211yescharacteristic, complemented
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2075C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic, complemented
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2065C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2011C2211yescharacteristic
119#1999C2211yescharacteristic
120#1985C2211yescharacteristic, complemented
121#1985C2211yescharacteristic, complemented
122#1982C2211yescharacteristic
123#1972C2211yescharacteristic
124#1972C2211yescharacteristic, complemented
125#1970C2211yescharacteristic
126#1970C2211yescharacteristic
127#1961C2211yescharacteristic
128#1961C2211yescharacteristic
129#1949C2211yescharacteristic, complemented
130#1949C2211yescharacteristic, complemented
131#1947C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic, complemented
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic, complemented
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1925C2211yescharacteristic, complemented
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic, complemented
172#1879C2211yescharacteristic, complemented
173#1879C2211yescharacteristic, complemented
174#1874C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1852C2211yescharacteristic
184#1847C2211yescharacteristic, complemented
185#1836C2211yescharacteristic, complemented
186#1817C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1802C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194C4×#106C2211yescharacteristic, complemented
195C4×#106C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207#551—48no—
208C2×#127C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#124—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8D411yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117—21no—
236C2×#117—21no—
237C22×C4⋊C4—21no—
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C42C2311yescharacteristic
243#459—24no—
244#447—24no—
245#442—24no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#399—21no—
308#399—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#392—21no—
330#392—21no—
331#391—21no—
332#391D411yescharacteristic
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389D411yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387D411yescharacteristic
384#387D411yescharacteristic
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#385—21no—
396#385—21no—
397#385D411yescharacteristic
398#385D411yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383—21no—
404#383—21no—
405#382—21no—
406#382—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#381—21no—
412#381—21no—
413#381—21no—
414#381—21no—
415#381—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380D411yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#379—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C25—21no—
483C22×Q8C2×D411yescharacteristic
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×D8—41no—
516C2×D8—41no—
517C2×D8—41no—
518C2×D8—41no—
519C2×D8#4114yes—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528#127—22no—
529#127—41no—
530#127—41no—
531#127—41no—
532#126—44no—
533#126—44no—
534#124—44no—
535#123—44no—
536#123—44no—
537#123—44no—
538#123—82no—
539C22⋊Q8—24no—
540C22⋊Q8—44no—
541C22⋊Q8—82no—
542#121—22no—
543#121—41no—
544#121—41no—
545#121—41no—
546#120—44no—
547#120—82no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—44no—
563C4×D4—44no—
564C4×D4—44no—
565#117—44no—
566#117—44no—
567#117—82no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—82no—
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—44no—
652C2×C22⋊C4—44no—
653C2×C22⋊C4—82no—
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—41no—
667C2×C42—41no—
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#107—41no—
677#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#106—22no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686#106—41no—
687#106—41no—
688#106—41no—
689C4⋊C8—22no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722C22⋊C8—41no—
723#97—22no—
724#97—41no—
725#97—41no—
726#97—41no—
727C4×C8—41no—
728C4×C8—41no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—42no—
774C24—42no—
775C24—42no—
776C24—42no—
777C24—81no—
778C24—81no—
779C24—81no—
780C24C22×D411yescharacteristic
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8—41no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—81no—
831C2×D4C2×#4112yes—
832C2×D4C2×#4112yes—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4AGL(1,ℤ/8)14yes—
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C2511yescharacteristic
892D8—44no—
893D8—82no—
894D8—82no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8C2×#4112yes—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—41no—
1028C42—41no—
1029C42—42no—
1030C42—42no—
1031C42—42no—
1032C42—42no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—22no—
1044C23—22no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—84no—
1072C23—84no—
1073C23—84no—
1074C23—84no—
1075C23—162no—
1076C23—162no—
1077C23—162no—
1078C23C2×AGL(1,ℤ/8)12yes—
1079C23C23×D411yescharacteristic
1080Q8—82no—
1081D4—22no—
1082D4—22no—
1083D4—22no—
1084D4—22no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—84no—
1098D4—84no—
1099D4—84no—
1100D4—84no—
1101D4—162no—
1102D4—162no—
1103D4—162no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—44no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—84no—
1183C2×C4—82no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4C2×AGL(1,ℤ/8)12yes—
1191C2×C4C2×AGL(1,ℤ/8)12yes—
1192C2×C4C22×#4111yescharacteristic
1193C2×C4#58511yescharacteristic
1194C2×C4#58511yescharacteristic
1195C2×C4#58511yescharacteristic
1196C2×C4#58511yescharacteristic
1197C2×C4#58511yescharacteristic
1198C8—22no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—168no—
1242C22D4×#4111yescharacteristic
1243C22#348511yescharacteristic
1244C22#348711yescharacteristic
1245C22C22×AGL(1,ℤ/8)11yescharacteristic
1246C22#358411yescharacteristic
1247C22#358511yescharacteristic
1248C22#358511yescharacteristic
1249C4—22no—
1250C4—22no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4#349111yescharacteristic
1275C4#352111yescharacteristic
1276C4#356611yescharacteristic
1277C4#356611yescharacteristic
1278C2—42no—
1279C2—82no—
1280C2—82no—
1281C2—161no—
1282C2—161no—
1283C2#4354811yescharacteristic
1284C2#6143711yescharacteristic
1285C2#6150511yescharacteristic
1286C2#6170711yescharacteristic
1287C2#6175111yescharacteristic
1288C2#6189011yescharacteristic
1289C2#6192411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31000C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59820C2semidirect
2. #59257C2semidirect
3. #32666C2semidirect
4. #32623C2semidirect
5. #32401C2semidirect
6. #32308C2semidirect
7. #31958C2semidirect
8. #31597C2semidirect
9. #31314C2semidirect
11. #29408C2semidirect
12. #29028C2semidirect
13. #28038C2semidirect
14. #27585C2semidirect
15. #27571C2semidirect
16. #27534C2semidirect
17. #27495C2semidirect
18. #27470C2semidirect
19. #27365C2semidirect
20. #27199C2semidirect
21. #27174C2semidirect
22. #26755C2semidirect
23. #26334C2semidirect
24. #26174C2semidirect
25. #25007C2semidirect
26. #24909C2semidirect
27. #23755C2semidirect
28. #23108C2semidirect
29. #22817C2semidirect
30. #22325C2semidirect
31. #22040C2semidirect
42. #2571C22semidirect
45. #2538C22semidirect
49. #2509C22semidirect
50. #2509C22semidirect
67. #2357C22semidirect
68. #2357C22semidirect
69. #2355C22semidirect
72. D4×C4⋊C4C22semidirect
80. #2101C22semidirect
81. #2100C22semidirect
82. #2100C22semidirect
85. #2094C22semidirect
86. #2094C22semidirect
89. #2092C22semidirect
90. #2088C22semidirect
91. #2085C22semidirect
92. #2084C22semidirect
93. #2084C22semidirect
94. #2084C22semidirect
100. #2073C22semidirect
103. #2071C22semidirect
107. #2065C22semidirect
108. #2065C22semidirect
109. #2065C22semidirect
120. #1985C22semidirect
121. #1985C22semidirect
124. #1972C22semidirect
129. #1949C22semidirect
130. #1949C22semidirect
131. #1947C22semidirect
132. #1944C22semidirect
133. #1944C22semidirect
137. #1936C22semidirect
145. #1926C22semidirect
149. #1925C22semidirect
150. #1925C22semidirect
151. #1925C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1919C22semidirect
159. #1919C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
171. #1879C22semidirect
172. #1879C22semidirect
173. #1879C22semidirect
176. #1864C22semidirect
179. #1862C22semidirect
180. #1862C22semidirect
184. #1847C22semidirect
185. #1836C22semidirect
189. #1802C22semidirect
193. #1776C22semidirect
194. C4×#106C22semidirect
195. C4×#106C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
199. #1762C22semidirect
200. C4×#102C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#598202
#592572
#326662
#326232
#324012
#323082
#319582
#315972
#313142
#310002
#294082
#290282
#280382
#275852
#275712
#275342
#274952
#274702
#273652
#271992
#271742
#267552
#263342
#261742
#250072
#249092
#237552
#231082
#228172
#223252
#220402